How to make a centered hexagon door consisting of 6 triangles?
For the modeling, here are 3 ways:

First the simplest way, if you don't need your triangles to be linked:


Create a circle (6 vertices, Fill Type > Triangle Fan).
Choose Edge Select mode, select all the concentric edges and press V to rip, then enter to validate right away. Now each triangle is independent.


If you want your triangles to be linked (so that you can continue to work its topology) you could use linked duplications:


Create a 3 vertices circle.
Put its origin on one of its vertices (or put the 3D cursor on one of its vertices and choose the 3D cursor as Pivot Center).
Duplicate your triangle with altD. Press enter to confirm right away.
Make your linked copy rotate 60° on the Z axis.
Make a second linked copy and make it rotate 120°, etc...


You could also use an Array modifier:


Create a 3 vertices circle.
Put its origin on one of its vertices.
Put an empty on the same point.
Give your triangle an Array modifier, and choose the empty as Object.
Rotate the empty 60° on the Z axis.




For the animation, you can do it this way:


Separate each triangle.
Set the origin on the geometry of each triangle with shiftctrlaltC.
Choose Pivot Point option > Median Point and enable the Manipulate Center Point option (don't forget to disable it when you'll have finished to keyframe).
In the Timeline, put your cursor at frame 0.
Select all your triangles and create a keyframe with i > LocRotScale.
In the Timeline, put your cursor at frame X.
With all your triangles selected, scale up with S. With the Manipulate Center Point option enabled the triangles will go away from each others instead of scaling.
Create a new keyframe with i > LocRotScale.